Decide Whether The Ordered Pair { (3,7)$}$ Is A Solution Of The Equation { X-y=-4$}$.Is { (3,7)$}$ A Solution Of { X-y=-4$}$?A. Yes B. No

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Understanding the Equation and the Ordered Pair

To determine whether the ordered pair (3,7) is a solution of the equation x-y=-4, we need to understand the concept of a solution in the context of linear equations. A solution to an equation is an ordered pair of values that makes the equation true. In this case, we are given the equation x-y=-4 and the ordered pair (3,7).

Substituting the Ordered Pair into the Equation

To check if the ordered pair (3,7) is a solution of the equation x-y=-4, we need to substitute the values of x and y from the ordered pair into the equation. This means we will replace x with 3 and y with 7 in the equation x-y=-4.

Performing the Substitution

Let's substitute x=3 and y=7 into the equation x-y=-4.

x - y = -4 3 - 7 = -4

Evaluating the Result

Now, let's evaluate the result of the substitution. We have 3 - 7 = -4. This is a true statement, as the result of subtracting 7 from 3 is indeed -4.

Conclusion

Based on the substitution and evaluation, we can conclude that the ordered pair (3,7) is a solution of the equation x-y=-4. This means that when x=3 and y=7, the equation x-y=-4 is true.

Why is this Important?

Understanding whether an ordered pair is a solution of an equation is crucial in mathematics, particularly in algebra and geometry. It helps us to verify the validity of equations and to solve problems involving linear equations.

Real-World Applications

The concept of solutions to linear equations has numerous real-world applications. For example, in economics, linear equations are used to model the relationship between variables such as supply and demand. In physics, linear equations are used to describe the motion of objects.

Tips and Tricks

When working with linear equations, it's essential to remember the following tips and tricks:

  • Always substitute the values of x and y from the ordered pair into the equation.
  • Evaluate the result of the substitution to determine whether the ordered pair is a solution of the equation.
  • Use the concept of solutions to linear equations to verify the validity of equations and to solve problems involving linear equations.

Common Mistakes to Avoid

When working with linear equations, it's essential to avoid the following common mistakes:

  • Failing to substitute the values of x and y from the ordered pair into the equation.
  • Not evaluating the result of the substitution to determine whether the ordered pair is a solution of the equation.
  • Misinterpreting the concept of solutions to linear equations.

Conclusion

In conclusion, the ordered pair (3,7) is a solution of the equation x-y=-4. This means that when x=3 and y=7, the equation x-y=-4 is true. Understanding whether an ordered pair is a solution of an equation is crucial in mathematics, particularly in algebra and geometry. It helps us to verify the validity of equations and to solve problems involving linear equations.

Final Answer

The final answer is: A. Yes

Q: What is a solution to a linear equation?

A: A solution to a linear equation is an ordered pair of values that makes the equation true. In other words, it is a pair of values that satisfies the equation.

Q: How do I determine whether an ordered pair is a solution of a linear equation?

A: To determine whether an ordered pair is a solution of a linear equation, you need to substitute the values of x and y from the ordered pair into the equation and evaluate the result. If the result is true, then the ordered pair is a solution of the equation.

Q: What is the difference between a solution and a point on a graph?

A: A solution to a linear equation is an ordered pair of values that makes the equation true, whereas a point on a graph is a pair of coordinates that represents a location on the graph. While a solution to an equation can be a point on a graph, not all points on a graph are solutions to the equation.

Q: Can an ordered pair be a solution to more than one linear equation?

A: Yes, an ordered pair can be a solution to more than one linear equation. For example, the ordered pair (3,7) is a solution to both the equations x-y=-4 and x-y=2.

Q: How do I find the solution to a linear equation?

A: To find the solution to a linear equation, you need to solve the equation for one variable in terms of the other variable. This can be done using various methods such as substitution, elimination, or graphing.

Q: What is the significance of solutions to linear equations in real-world applications?

A: Solutions to linear equations have numerous real-world applications in fields such as economics, physics, and engineering. They are used to model the relationship between variables, make predictions, and solve problems.

Q: Can a linear equation have no solution?

A: Yes, a linear equation can have no solution. This occurs when the equation is inconsistent, meaning that it is impossible to find a pair of values that satisfies the equation.

Q: How do I determine whether a linear equation has a solution or not?

A: To determine whether a linear equation has a solution or not, you need to check if the equation is consistent or inconsistent. If the equation is consistent, then it has a solution. If the equation is inconsistent, then it has no solution.

Q: What is the relationship between solutions to linear equations and the graph of a linear equation?

A: The solutions to a linear equation are the points on the graph of the equation that satisfy the equation. In other words, the solutions to a linear equation are the points on the graph that make the equation true.

Q: Can a linear equation have an infinite number of solutions?

A: Yes, a linear equation can have an infinite number of solutions. This occurs when the equation is an identity, meaning that it is true for all values of the variables.

Q: How do I determine whether a linear equation has an infinite number of solutions or not?

A: To determine whether a linear equation has an infinite number of solutions or not, you need to check if the equation is an identity or not. If the equation is an identity, then it has an infinite number of solutions. If the equation is not an identity, then it has a finite number of solutions.

Conclusion

In conclusion, solutions to linear equations are an essential concept in mathematics, particularly in algebra and geometry. They have numerous real-world applications and are used to model the relationship between variables, make predictions, and solve problems. Understanding solutions to linear equations is crucial in mathematics and is a fundamental concept that is used in various fields.